www.pudn.com > gmm_utilities.zip > gmm_derivative.m

function J = gmm_derivative(g, s, numerical) 
%function J = gmm_derivative(g, s, numerical) 
% 
% INPUTS: 
%   g - gmm 
%   s - set of N samples from the domain of g 
%   numerical - if 1 then compute Jacobians via numerical approximation, 
%       else the default is an analytical solution. 
% 
% OUTPUT: 
%   J - Jacobian of g with respect to s. The i-th row of J is dg/ds(:,i), 
%       such that J is (N x D), where D is the gmm domain dimension. 
% 
% REFERENCES: 
%   Ridley, M.F., Generalised Bayesian Estimation for Decentralised Sensor 
%       Networks, University of Sydney, Australian Centre for Field 
%       Robotics, 2005. 
%   Williams, J.L., Gaussian Mixture Reduction for Tracking Multiple 
%       Maneuvering Targets in Clutter, Masters thesis, Air Force Institute 
%       of Technology, Wright-Patterson Air Force Base, 2003. 
% 
% Compute the Jacobian dg/ds at each point s.  
% 
% Tim Bailey 2006. 
 
if nargin == 2, numerical = 0; end 
 
[D,N] = size(s); 
if numerical ~= 1 
    % Analytical Jacobian as described in Ridley, p169, and Williams, p3-29 
    J = zeros(N,D); 
    for i=1:length(g.w) 
        v = s - repvec(g.x(:,i), N); 
        w = gauss_evaluate(v, g.P(:,:,i)); 
        J = J - g.w(i) * v' * inv(g.P(:,:,i)) .* repvec(w(:), D);  
    end         
     
else 
    % Numerical Jacobian approximation 
    for i=1:N 
        J(i,:) = numerical_Jacobian(s(:,i), @jacmodel, [], [], g); 
    end 
end 
 
% 
% 
 
function f = jacmodel(s, g) 
f = gmm_evaluate(g, s);